We explore the physical origin and robustness of constraints on the energy density in relativistic species prior to and during recombination, often expressed as constraints on an effective number of neutrino species, $N_{\mathrm{eff}}$. If the primordial helium abundance, $Y_{\mathrm{P}}$, follows the prediction of the big bang nucleosynthesis (BBN) theory, the constraint on $N_{\mathrm{eff}}$ from current cosmic microwave background anisotropy data is almost entirely due to the impact of the neutrinos on the expansion rate, and how those changes to the expansion rate alter the ratio of the photon diffusion scale to the sound horizon scale at recombination. We demonstrate that, as long as the primordial helium abundance is derived in a BBN-consistent manner, the constraint on $N_{\mathrm{eff}}$ degrades little after marginalizing over $A_{\mathrm{eISW}}$, the phenomenological parameter characterizing the amplitude of the early Integrated Sachs-Wolfe (ISW) effect. We also provide a first determination of $A_{\mathrm{eISW}}$. Varying the $Y_{\mathrm{P}}$ also changes the ratio of damping to sound horizon scales. We study the physical effects that prevent the resulting near degeneracy between $N_{\mathrm{eff}}$ and $Y_{\mathrm{P}}$ from being a complete one and find that the early ISW effect does play a role in breaking this degeneracy. Examining light-element abundance measurements, we see no significant evidence for the evolution of $N_{\mathrm{eff}}$ and the baryon-to-photon ratio from the epoch of BBN to decoupling. Finally, we consider measurements of the distance-redshift relation at low to intermediate redshifts and their implications for the value of $N_{\mathrm{eff}}$.

• Received 12 April 2011

DOI:https://doi.org/10.1103/PhysRevD.87.083008